Sure! Let's identify the numbers from the given set that fit each of the four descriptions.
### Given Set of Numbers:
[tex]\[
\{21, 20, 25, 11, 8, 6, 10, 15, 32\}
\][/tex]
### (a) A multiple of 4 and a multiple of 5
To fit both these criteria, the number must be divisible by both 4 and 5. Only one number satisfies this condition from the given set.
- Answer: [tex]\( 20 \)[/tex]
### (b) A square number and an odd number
A square number is a number that can be expressed as [tex]\( n^2 \)[/tex] where [tex]\( n \)[/tex] is an integer. Additionally, it must be an odd number.
- Answer: [tex]\( 25 \)[/tex] (since [tex]\( 25 = 5^2 \)[/tex] and 25 is odd)
### (c) A factor of 24 and a factor of 30
The number must divide both 24 and 30 without leaving a remainder.
- Answer: [tex]\( 6 \)[/tex] (since [tex]\( 24 \div 6 = 4 \)[/tex] and [tex]\( 30 \div 6 = 5 \)[/tex])
### (d) A multiple of 5 and a factor of 20
The number must be divisible by 5 and also divide 20 without leaving a remainder.
- Answer: [tex]\( 20 \)[/tex]
So, consolidating all the answers:
[tex]\[
(a) \ 20
\][/tex]
[tex]\[
(b) \ 25
\][/tex]
[tex]\[
(c) \ 6
\][/tex]
[tex]\[
(d) \ 20
\][/tex]
Hence, the numbers chosen from the box that fit each description are as follows:
- (a) 20
- (b) 25
- (c) 6
- (d) 20
